Nematic Quantum Critical Point Research Articles

Highly anisotropic superconducting gap near the nematic quantum critical point of FeSe1−xSx

Highly anisotropic superconducting gap near the nematic quantum critical point of FeSe1−xSx

Valley-polarized nematic order in twisted moiré systems: In-plane orbital magnetism and crossover from non-Fermi liquid to Fermi liquid

The interplay between strong correlations and non-trivial topology in twisted moir\'e systems can give rise to a rich landscape of ordered states that intertwine the spin, valley, and charge degrees of freedom. In this paper, we investigate the properties of a system that displays long-range valley-polarized nematic order. Besides breaking the threefold rotational symmetry of the triangular moir\'e superlattice, this type of order also breaks twofold rotational and time-reversal symmetries, which leads to interesting properties. First, we develop a phenomenological model to describe the onset of this ordered state in twisted moir\'e systems and to explore its signatures in their thermodynamic and electronic properties. Its main manifestation is that it triggers the emergence of in-plane orbital magnetic moments oriented along high-symmetry lattice directions. We also investigate the properties of the valley-polarized nematic state at zero temperature. Due to the existence of a dangerously irrelevant coupling $\lambda$ in the six-state clock model that describes the putative valley-polarized nematic quantum critical point, the ordered state displays a pseudo-Goldstone mode. Using a two-patch model, we compute the fermionic self-energy to show that down to very low energies, the Yukawa-like coupling between the pseudo-Goldstone mode and the electronic degrees of freedom promotes the emergence of non-Fermi liquid behavior. Below a crossover energy scale $\Omega^{*}\sim\lambda^{3/2}$, however, Fermi liquid behavior is recovered. Finally, we discuss the applicability of these results to other non-trivial nematic states, such as the spin-polarized nematic phase.

Enhanced Superconducting Pairing Strength near a Pure Nematic Quantum Critical Point

The quest for high-temperature superconductivity at ambient pressure is a central issue in physics. In this regard, the relationship between unconventional superconductivity and the quantum critical point (QCP) associated with the suppression of some form of symmetry-breaking order to zero temperature has received particular attention. The key question is how the strength of the electron pairs changes near the QCP, and this can be verified by high-field experiments. However, such studies are limited mainly to superconductors with magnetic QCPs, and the possibility of unconventional mechanisms by which nonmagnetic QCP promotes strong pairing remains a nontrivial issue. Here, we report systematic measurements of the upper critical field $H_{{\rm c2}}$ in nonmagnetic FeSe$_{1-x}$Te$_{x}$ superconductors, which exhibit a QCP of electronic nematicity characterized by spontaneous rotational-symmetry breaking. As the magnetic field increases, the superconducting phase of FeSe$_{1-x}$Te$_{x}$ shrinks to a narrower dome surrounding the nematic QCP. The analysis of $H_{{\rm c2}}$ reveals that the Pauli-limiting field is enhanced toward the QCP, implying that the pairing interaction is significantly strengthened via nematic fluctuations emanated from the QCP. Remarkably, this nonmagnetic nematic QCP is not accompanied by a divergent effective mass, distinct from the magnetically mediated pairing. Our observation opens up a nonmagnetic route to high-temperature superconductivity.

Nematic-Fluctuation-Mediated Superconductivity Revealed by Anisotropic Strain in Ba(Fe_{1-x}Co_{x})_{2}As_{2}.

Anisotropic strain is an external field capable of selectively addressing the role of nematic fluctuations in promoting superconductivity. We demonstrate this using polarization-resolved elasto-Raman scattering by probing the evolution of nematic fluctuations under strain in the normal and superconducting state of the paradigmatic iron-based superconductor Ba(Fe_{1-x}Co_{x})_{2}As_{2}. In the parent compound BaFe_{2}As_{2} we observe a strain-induced suppression of the nematic susceptibility which follows the expected behavior of an Ising order parameter under a symmetry breaking field. For the superconducting compound, the suppression of the nematic susceptibility correlates with the decrease of the critical temperature T_{c}, indicating a significant contribution of nematic fluctuations to electron pairing. Our results validate theoretical scenarios of enhanced T_{c} near a nematic quantum critical point.

Superconductivity near a nematoelastic quantum critical point

We study the pairing instability of a two-dimensional metallic system induced by Ising-nematic quantum fluctuations in the presence of an unavoidable relevant coupling of the nematic order parameter to the elastic modes (acoustic phonons) of the lattice. We find that this nematoelastic coupling $\lambda_\mathrm{latt}$ leads to a decrease of both the superconducting (SC) critical temperature $T_c$ and the gap function $\Delta$, regardless of the gap symmetry. Interestingly, we show that $\lambda_\mathrm{latt}$ provides a knob that allows us to investigate the emergence of the SC phase at low temperatures, as an instability from either a non-Fermi liquid or a Fermi liquid normal state. The phase transitions between the SC and these normal states are characterized by different critical exponents, which may also vary for each gap symmetry. Finally, we argue that these results might explain the dependence of $T_c$ in the vicinity of the nematic quantum critical point exhibited by the compound FeSe$_{1 - x}$S$_x$.

Pure nematic quantum critical point accompanied by a superconducting dome

SignificanceThe notion of the quantum critical point (QCP) is at the core of modern condensed matter physics. Near a QCP of the symmetry-breaking order, associated quantum-mechanical fluctuations are intensified, which can lead to unconventional superconductivity. Indeed, dome-shaped superconducting phases are often observed near the magnetic QCPs, which supports the spin fluctuation-driven superconductivity. However, the fundamental question remains as to whether a nonmagnetic QCP of electronic nematic order characterized by spontaneous rotational symmetry breaking can promote superconductivity in real materials. Here, we provide an experimental demonstration that a pure nematic QCP exists near the center of a superconducting dome in nonmagnetic FeSe[Formula: see text] Tex. This result evidences that nematic fluctuations enhanced around the nematic QCP can boost superconductivity.

Transport evidence for decoupled nematic and magnetic criticality in iron chalcogenides

Electronic nematicity in correlated metals often occurs alongside another instability such as magnetism. The question thus remains whether nematicity alone can drive unconventional superconductivity or anomalous (quantum critical) transport in such systems. In FeSe, nematicity emerges in isolation, providing a unique opportunity to address this question. Studies to date, however, have proved inconclusive; while signatures of nematic criticality are observed upon sulfur substitution, they appear to be quenched by the emergent magnetism under the application of pressure. Here, we study the temperature and pressure dependence of the low-temperature resistivity of FeSe1-xSx crystals at x values beyond the nematic quantum critical point. Two distinct components to the resistivity are revealed; one that is suppressed with increasing pressure and one that grows upon approaching the magnetic state at higher pressures. These findings hint that nematic and magnetic critical fluctuations in FeSe1-xSx are completely decoupled, in marked contrast to other Fe-based superconductors.

Comparison of temperature and doping dependence of elastoresistivity near a putative nematic quantum critical point

Strong electronic nematic fluctuations have been discovered near optimal doping for several families of Fe-based superconductors, motivating the search for a possible link between these fluctuations, nematic quantum criticality, and high temperature superconductivity. Here we probe a key prediction of quantum criticality, namely power-law dependence of the associated nematic susceptibility as a function of composition and temperature approaching the compositionally tuned putative quantum critical point. To probe the ‘bare’ quantum critical point requires suppression of the superconducting state, which we achieve by using large magnetic fields, up to 45 T, while performing elastoresistivity measurements to follow the nematic susceptibility. We performed these measurements for the prototypical electron-doped pnictide, Ba(Fe1−xCox)2As2, over a dense comb of dopings. We find that close to the putative quantum critical point, the elastoresistivity appears to obey power-law behavior as a function of composition over almost a decade of variation in composition. Paradoxically, however, we also find that the temperature dependence for compositions close to the critical value cannot be described by a single power law.

Hidden Nematic Quantum Critical Point and Precursor to Mott Insulating State with 3d5 Electron Configuration in Iron-Based Superconductors

Hidden Nematic Quantum Critical Point and Precursor to Mott Insulating State with 3d⁵ Electron Configuration in Iron-Based Superconductors

Signatures of a Quantum Griffiths Phase Close to an Electronic Nematic Quantum Phase Transition.

In the vicinity of a quantum critical point, quenched disorder can lead to a quantum Griffiths phase, accompanied by an exotic power-law scaling with a continuously varying dynamical exponent that diverges in the zero-temperature limit. Here, we investigate a nematic quantum critical point in the iron-based superconductor FeSe_{0.89}S_{0.11} using applied hydrostatic pressure. We report an unusual crossing of the magnetoresistivity isotherms in the nonsuperconducting normal state that features a continuously varying dynamical exponent over a large temperature range. We interpret our results in terms of a quantum Griffiths phase caused by nematic islands that result from the local distribution of Se and S atoms. At low temperatures, the Griffiths phase is masked by the emergence of a Fermi liquid phase due to a strong nematoelastic coupling and a Lifshitz transition that changes the topology of the Fermi surface.

Specific Heat of a Quantum Critical Metal.

We investigate the specific heat c, near an Ising nematic quantum critical point (QCP), using sign problem-free quantum MonteCarlo simulations. Cooling towards the QCP, we find a broad regime of temperature where c/T is close to the value expected from the noninteracting band structure, even for a moderately large coupling strength. At lower temperature, we observe a rapid rise of c/T, followed by a drop to zero as the system becomes superconducting. The spin susceptibility begins to drop at roughly the same temperature where the enhancement of c/T onsets, most likely due to the opening of a gap associated with superconducting fluctuations. These findings suggest that superconductivity and non-Fermi liquid behavior (manifested in an enhancement of the effective mass) onset at comparable energy scales. We support these conclusions with an analytical perturbative calculation.

Putative Hall response of the strange metal component in FeSe1−xSx

The authors show that the Hall response of the electron nematic FeSe${}_{1\ensuremath{-}x}$S${}_{x}$ comprises two metal components, one of which shows an anomalous 1/T temperature dependence and peaking near the nematic quantum critical point.

Lattice-shifted nematic quantum critical point in FeSe1\u2212xSx

We report the evolution of nematic fluctuations in FeSe1−xSx single crystals as a function of Sulfur content x across the nematic quantum critical point (QCP) xc ~ 0.17 via Raman scattering. The Raman spectra in the B1g nematic channel consist of two components, but only the low energy one displays clear fingerprints of critical behavior and is attributed to itinerant carriers. Curie–Weiss analysis of the associated nematic susceptibility indicates a substantial effect of nemato-elastic coupling, which shifts the location of the nematic QCP. We argue that this lattice-induced shift likely explains the absence of any enhancement of the superconducting transition temperature at the QCP. The presence of two components in the nematic fluctuations spectrum is attributed to the dual aspect of electronic degrees of freedom in Hund’s metals, with both itinerant carriers and local moments contributing to the nematic susceptibility.

Non-Fermi liquid transport in the vicinity of the nematic quantum critical point of superconducting FeSe1−xSx

Non-Fermi liquids are strange metals whose physical properties deviate qualitatively from those of conventional metals due to strong quantum fluctuations. In this paper, we report transport measurements on the FeSe$_{1-x}$S$_x$ superconductor, which has a quantum critical point of a nematic order without accompanying antiferromagnetism. We find that in addition to a linear-in-temperature resistivity $\rho_{xx}\propto T$, which is close to the Planckian limit, the Hall angle varies as $\cot \theta_{\rm H} \propto T^2$ and the low-field magnetoresistance is well scaled as $\Delta\rho_{xx}/\rho_{xx}\propto \tan^2 \theta_{\rm H}$ in the vicinity of the nematic quantum critical point. This set of anomalous charge transport properties shows striking resemblance with those reported in cuprate, iron-pnictide and heavy fermion superconductors, demonstrating that the critical fluctuations of a nematic order with ${\bf q} \approx 0$ can also lead to a breakdown of the Fermi liquid description.

Suppression of superconductivity by anisotropic strain near a nematic quantum critical point

High temperature superconductivity emerges in the vicinity of competing strongly correlated phases. In the iron-based superconductor $Ba(Fe_{1-x}Co_{x})_{2}As_{2}$, the superconducting state shares the composition-temperature phase diagram with an electronic nematic phase and an antiferromagnetic phase that break the crystalline rotational symmetry. Symmetry considerations suggest that anisotropic strain can enhance these competing phases and thus suppress the superconductivity. Here we study the effect of anisotropic strain on the superconducting transition in single crystals of $Ba(Fe_{1-x}Co_{x})_{2}As_{2}$ through electrical transport, magnetic susceptibility, and x-ray diffraction measurements. We find that in the underdoped and near-optimally doped regions of the phase diagram, the superconducting critical temperature is rapidly suppressed by both compressive and tensile stress, and in the underdoped case this suppression is enough to induce a strain-tuned superconductor to metal quantum phase transition.

Evolution of the Nematic Susceptibility in LaFe_{1-x}Co_{x}AsO.

We report a systematic elastoresistivity study on LaFe_{1-x}Co_{x}AsO single crystals, which have well separated structural and magnetic transition lines. All crystals show a Curie-Weiss-like nematic susceptibility in the tetragonal phase. The extracted nematic temperature is monotonically suppressed upon cobalt doping, and changes sign around the optimal doping level, indicating a possible nematic quantum critical point beneath the superconducting dome. The amplitude of the nematic susceptibility shows a peculiar double-peak feature. This could be explained by a combined effect of different contributions to the nematic susceptibility, which are amplified at separated doping levels of LaFe_{1-x}Co_{x}AsO.

Divergent Nematic Susceptibility near the Pseudogap Critical Point in a Cuprate Superconductor

Superconductivity is a quantum phenomenon caused by bound pairs of electrons. In diverse families of strongly correlated electron systems, the electron pairs are not bound together by phonon exchange but instead by some other kind of bosonic fluctuations. In these systems, superconductivity is often found near a magnetic quantum critical point (QCP) where a magnetic phase vanishes in the zero-temperature limit. Moreover, the maximum of superconducting transition temperature Tc frequently locates near the magnetic QCP, suggesting that the proliferation of critical spin fluctuations emanating from the QCP plays an important role in Cooper pairing. In cuprate superconductors, however, the superconducting dome is usually separated from the antiferromagnetic phase and Tc attains its maximum value near the verge of enigmatic pseudogap state that appears below doping-dependent temperature T*. Thus a clue to the pairing mechanism resides in the pseudogap and associated anomalous transport properties. Recent experiments suggested a phase transition at T*, yet, most importantly, relevant fluctuations associated with the pseudogap have not been identified. Here we report on direct observations of enhanced nematic fluctuations in (Bi,Pb)2Sr2CaCu2O8+d by elastoresistance measurements, which couple to twofold in-plane electronic anisotropy, i.e. electronic nematicity. The nematic susceptibility shows Curie-Weiss-like temperature dependence above T*, and an anomaly at T* evidences a second-order transition with broken rotational symmetry. Near the pseudogap end point, where Tc is not far from its peak in the superconducting dome, nematic susceptibility becomes singular and divergent, indicating the presence of a nematic QCP. This signifies quantum critical fluctuations of a nematic order, which has emerging links to the high-Tc superconductivity and strange metallic behaviours in cuprates.

DC resistivity near a nematic quantum critical point: Effects of weak disorder and acoustic phonons

We calculate the resistivity associated with an Ising-nematic quantum critical point in the presence of disorder and acoustic phonons in the lattice model. To perform this analysis, we use the memory-matrix transport theory, which has a crucial advantage compared to other methods of not relying on the existence of well-defined quasiparticles in the low-energy effective theory. As a result, we obtain that by including an inevitable interaction between the nematic fluctuations and the elastic degrees of freedom of the lattice (parametrized by the nemato-elastic coupling κlatt), the resistivity ρ(T) of the system as a function of temperature obeys a universal scaling form described by ρ(T)∼Tln(1∕T) at high temperatures, reminiscent of the paradigmatic strange metal regime observed in many strongly correlated compounds. For a window of temperatures comparable with κlatt3∕2εF (where εF is the Fermi energy of the microscopic model), the system displays another regime in which the resistivity is consistent with a description in terms of ρ(T)∼Tα, where the effective exponent roughly satisfies the inequality 1≲α≲2. However, in the low-temperature limit (i.e., T≪κlatt3∕2εF), the properties of the quantum critical state change in an important way depending on the types of disorder present in the system: It can either recover a Fermi-liquid-like regime described by ρ(T)∼T2 or it could exhibit yet another non-Fermi liquid regime characterized by the scaling form ρ(T)−ρ0∼T2lnT (implying in the latter case that the system would display a Kondo-like upturn in the resistivity). From a broader perspective, our results emphasize the key role played by both phonon and disorder effects in the scenario of nematic quantum criticality and might be fundamental for addressing recent transport experiments in some iron-based superconductors.

Spatial nematic fluctuation in BaFe2(As1−xPx)2 revealed by spatially and angle-resolved photoemission spectroscopy

Nematicity, where rotational symmetry is broken while translational symmetry is conserved, is prevalent in high-temperature superconductors. In particular, nematic quantum critical point has been universally found near the optimum doping of the superconducting dome of several iron-based superconductor families. In such a regime, evidence for strong nematic fluctuations have been observed. As the precursor to this order, nematic fluctuations emerge before nematicity, providing favorable ground to study how nematic order modifies the electronic structure in the absence of structural distortion. Here we use spatially resolved angle-resolved photoemission spectroscopy to investigate the correlation between the onset of nematic fluctuations and electronic structure in an optimally doped ${\mathrm{BaFe}}_{2}{({\mathrm{As}}_{1\ensuremath{-}x}{\mathrm{P}}_{x})}_{2}$ ($x\phantom{\rule{0.222222em}{0ex}}\ensuremath{\sim}\phantom{\rule{0.222222em}{0ex}}0.3$) superconductor. We reveal a strong spatially varying anisotropy of the Fermi surface on a length scale of tens of microns with strong correlation between the changes in the hole and electron Fermi pockets, consistent with the variations expected in the presence of fluctuating nematic order. These results provide direct evidence for spatial nematic fluctuations in the optimal doping regime of iron-based superconductors.

Nematic fluctuations in the cuprate superconductor Bi2Sr2CaCu2O8+\u03b4

Establishing the presence and the nature of a quantum critical point in their phase diagram is a central enigma of the high-temperature superconducting cuprates. It could explain their pseudogap and strange metal phases, and ultimately their high superconducting temperatures. Yet, while solid evidences exist in several unconventional superconductors of ubiquitous critical fluctuations associated to a quantum critical point, in the cuprates they remain undetected until now. Here using symmetry-resolved electronic Raman scattering in the cuprate {mathrm{Bi}}_2{mathrm{Sr}}_2{mathrm{CaCu}}_2{mathrm{O}}_{8+delta}, we report the observation of enhanced electronic nematic fluctuations near the endpoint of the pseudogap phase. While our data hint at the possible presence of an incipient nematic quantum critical point, the doping dependence of the nematic fluctuations deviates significantly from a canonical quantum critical scenario. The observed nematic instability rather appears to be tied to the presence of a van Hove singularity in the band structure.